This week we’ll cover a few packages for visualizing our data:

library(tidyverse)
library(timetk)
library(plotly)
library(readxl)
library(janitor)
library(lubridate)

knitr::opts_chunk$set(message = FALSE, warning = FALSE, comment = NA)

Let’s load our HPI dataset, wrangle it, and pivot it into long format.

url <- "https://www.fhfa.gov/DataTools/Downloads/Documents/HPI/HPI_PO_monthly_hist.xls"

destfile <- "hpi.xls"

curl::curl_download(url, destfile)

hpi <- read_excel(destfile, skip = 3)

hpi_wrangled <- hpi %>% 
  clean_names() %>% 
  slice(-1) %>%   # remove empty row
  rename(date = month) %>%
  select(date, ends_with("_sa")) %>%  # only keep seasonally adj. data
  # separate() from tidyr package to split date into separate columns for day/month/year 
  separate(date, into = c("year", "month", "day"), sep = '-', convert = TRUE, remove = FALSE) %>% 
  # unite() from tidyr to join columns 
  unite(yr_mon, year, month, sep = "/", remove = FALSE) %>% 
  mutate_if(is.numeric, round, digits = 2) %>%  # round all numeric columns to 2 digits
  # add labels with case_when()
  mutate(season = case_when(between(month, 3, 5) ~ "spring",
                            between(month, 6, 8) ~ "summer",
                            between(month, 9, 11) ~ "fall",
                            # between(month, 12, 2) ~ "winter" == won't work because there's no numbers between 12 and 2
                            TRUE ~ "winter")) %>% 
  select(date, yr_mon, year, month, day, season, everything()) %>%  # reorder columns
  # arrange() from dplyr to sort rows
  arrange(date)

hpi_tidy <- 
  hpi_wrangled %>% 
  select(date, contains("north"), contains("south")) %>% 
  # pivot_longer makes data long, or tidy
  pivot_longer(-date, names_to = "division", values_to = "hpi") %>% 
  group_by(division)

hpi_tidy

ggplot2

And now let’s create a basic ggplot.

ggplot(hpi_tidy, aes(x = date, y = hpi, color = division)) +
  geom_line()

The ggplot2 package uses some unique syntax (the “grammar of graphics”) that allows us to create highly customizable static graphics. This grammar can be a bit hard to grasp, so don’t worry if it takes a while to “click”.

I think about ggplot like this:

Let’s dissect the code above to understand each step.

Wait, why a + instead of %>%? You can think of ggplots in layers. At each step, we’re adding a new layer, like we’re painting on a canvas. This is different than the pipe, which is for passing an object along to a new function.

Faceting

Another thing we can “add” to our ggplots is a faceting layer. Facets divide a plot into subplots based on one of our variables. For example:

ggplot(hpi_tidy, aes(x = date, y = hpi, color = division)) +
  geom_line() +
  facet_wrap(~division)

Scatterplot

There are many kinds of geoms we can add. For example, a scatterplot uses geom_point().

hpi_pct <- 
  hpi_tidy %>% 
  mutate(pct_change = (hpi / lag(hpi)) - 1,
         pct_change_12_mons = (hpi / lag(hpi, 12)) - 1) %>%
  na.omit()

hpi_pct %>% 
ggplot(aes(x = pct_change_12_mons, y = pct_change, color = division)) +
  geom_point() + #alpha = .5
  facet_wrap(~division, ncol = 4) +
  labs(x = "% change (1 mo.)", y = "% change (1 yr.)") +
  theme(legend.position = "none",
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        plot.title = element_text(hjust = 0.5))

Scatterplot with trend line

We can also add multiple geoms to a ggplot object, e.g. adding a trend line to our scatterplots:

hpi_pct %>% 
ggplot(aes(x = pct_change_12_mons, y = pct_change, color = division)) +
  geom_point() + #alpha = .5
  geom_smooth(method = "lm",  se = TRUE, color = "purple") +
  facet_wrap(~division, ncol = 4) +
  labs(x = "% change (1 mo.)", y = "% change (1 yr.)") +
  theme(legend.position = "none",
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        plot.title = element_text(hjust = 0.5))

Histogram

There are lots of ways to customize the look and feel of your plots:

hpi_pct %>% 
  ggplot(aes(x = pct_change)) +
  geom_histogram(fill = "darkblue", color = "darkred", bins = 50) +
  facet_wrap(~division) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  theme_minimal()

Density

hpi_pct %>% 
  ggplot(aes(x = pct_change)) +
  geom_density(fill = "darkblue", color = "darkred", bins = 50) +
  facet_wrap(~division) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  theme_minimal()

Histogram and Density

hpi_pct %>% 
  ggplot(aes(x = pct_change)) +
  geom_histogram(fill = "darkblue", color = "darkred", bins = 20) +
  geom_density(color = "red") +
  facet_wrap(~division) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))

Shading for recession

We can even combine datasets on the same plot. Let’s create a geom to shade the background of a plot during recession periods.

# First, create our recessions tibble with tribble()
recessions <- 
tribble(
  ~Peak, ~Trough,
  "1948-11-01", "1949-10-01",
  "1953-07-01", "1954-05-01",
  "1957-08-01", "1958-04-01",
  "1960-04-01", "1961-02-01",
  "1969-12-01", "1970-11-01",
  "1973-11-01", "1975-03-01",
  "1980-01-01", "1980-07-01",
  "1981-07-01", "1982-11-01",
  "1990-07-01", "1991-03-01",
  "2001-03-01", "2001-11-01",
  "2007-12-01", "2009-06-01",
  "2020-02-01", "2020-05-01"
  ) %>% 
  mutate(Peak = ymd(Peak),
         Trough = ymd(Trough))


recession_shade <- 
  geom_rect(data = recessions, 
            inherit.aes = F, 
            aes(xmin = Peak, 
                xmax = Trough, 
                ymin = -Inf, 
                ymax = +Inf), 
            fill = 'pink', 
            alpha = 0.5)


hpi_pct %>% 
  ggplot(aes(x = ymd(date), y = pct_change, color = division)) +
  recession_shade +
  geom_line() +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1),
        plot.title = element_text(hjust = 0.5),
        plot.subtitle = element_text(hjust = 0.5),
        plot.caption = element_text(hjust=0)) +
  ylab("") +
  xlab("Percent change, monthly") +
  ggtitle("Housing Price Appreciation", 
          subtitle = "by US Census Division") +
  labs(caption = "data source: FHFA") +
  scale_x_date(limits = c(as.Date(min(hpi_pct$date)), as.Date(max(hpi_pct$date)))) 

timetk for time series data

The timetk package includes a bunch of functions that make working with time series data super easy. This includes functions for easily creating great looking plots of time series data:

hpi_pct %>% 
  ungroup() %>% 
  plot_time_series(date, pct_change, .color_var = division, .smooth = FALSE)

Anomaly diagnostics with timetk

timetk also includes functions for automatic anomaly detection:

hpi_pct %>% 
  filter(division == "south_atlantic_sa") %>% 
  ungroup() %>% 
  plot_anomaly_diagnostics(date, pct_change)

Plotly and ggplotly()

timetk’s interactive plots rely on plotly, a library for building interactive JavaScript visualizations. Plotly is supported in several different languages (including R) and has its own syntax.

Importantly, the plotly R package includes a function called ggplotly() that (you guessed it!) turns ggplots into plotly charts.

---
title: "Data Visualization"
output: html_notebook
---

This week we'll cover a few packages for visualizing our data:

* [`ggplot2`](https://ggplot2.tidyverse.org/), our main package for static data visualization with the tidyverse
* [`timetk`](https://business-science.github.io/timetk/index.html), a package built by Matt Dancho for working with time series data
* [`plotly`](https://github.com/ropensci/plotly), an interactive visualization builder that also integrates nicely with ggplot.

```{r setup, message = FALSE, warning = FALSE}
library(tidyverse)
library(timetk)
library(plotly)
library(readxl)
library(janitor)
library(lubridate)

knitr::opts_chunk$set(message = FALSE, warning = FALSE, comment = NA)
```


Let's load our HPI dataset, wrangle it, and pivot it into long format.

```{r}
hpi <- read_excel("HPI_PO_monthly_hist.xls", skip = 3)

hpi_wrangled <- hpi %>% 
  clean_names() %>% 
  slice(-1) %>%   # remove empty row
  rename(date = month) %>%
  select(date, ends_with("_sa")) %>%  # only keep seasonally adj. data
  # separate() from tidyr package to split date into separate columns for day/month/year 
  separate(date, into = c("year", "month", "day"), sep = '-', convert = TRUE, remove = FALSE) %>% 
  # unite() from tidyr to join columns 
  unite(yr_mon, year, month, sep = "/", remove = FALSE) %>% 
  mutate_if(is.numeric, round, digits = 2) %>%  # round all numeric columns to 2 digits
  # add labels with case_when()
  mutate(season = case_when(between(month, 3, 5) ~ "spring",
                            between(month, 6, 8) ~ "summer",
                            between(month, 9, 11) ~ "fall",
                            # between(month, 12, 2) ~ "winter" == won't work because there's no numbers between 12 and 2
                            TRUE ~ "winter")) %>% 
  select(date, yr_mon, year, month, day, season, everything()) %>%  # reorder columns
  # arrange() from dplyr to sort rows
  arrange(date)

hpi_tidy <- 
  hpi_wrangled %>% 
  select(date, contains("north"), contains("south")) %>% 
  # pivot_longer makes data long, or tidy
  pivot_longer(-date, names_to = "division", values_to = "hpi") %>% 
  group_by(division)

hpi_tidy
```

# `ggplot2`

And now let's create a basic `ggplot`.

```{r}
ggplot(hpi_tidy, aes(x = date, y = hpi, color = division)) +
  geom_line()
```

The `ggplot2` package uses some unique syntax (the "grammar of graphics") that allows us to create highly customizable static graphics. This grammar can be a bit hard to grasp, so don't worry if it takes a while to "click".

I think about ggplot like this:

* We always start by calling `ggplot()` to create our plot object. This is (usually!) where we will specify our data and *aesthetic mappings*, or how our variables should map onto features of the plot like axes, colored groupings, etc.
* Then we add *geoms* to our plot. This is the step that will actually display our data on the graph. We will always have at least one of these, and sometimes multiple.
* Finally, we can change the appearance of our plot by adding things like *themes* and changing titles and captions.

Let's dissect the code above to understand each step.

Wait, why a `+` instead of `%>%`? You can think of ggplots in layers. At each step, we're adding a new layer, like we're painting on a canvas. This is different than the pipe, which is for passing an object along to a new function.


## Faceting

Another thing we can "add" to our ggplots is a faceting layer. Facets divide a plot into subplots based on one of our variables. For example:

```{r}
ggplot(hpi_tidy, aes(x = date, y = hpi, color = division)) +
  geom_line() +
  facet_wrap(~division)
```



## Scatterplot

There are many kinds of geoms we can add. For example, a scatterplot uses `geom_point()`.

```{r}
hpi_pct <- 
  hpi_tidy %>% 
  mutate(pct_change = (hpi / lag(hpi)) - 1,
         pct_change_12_mons = (hpi / lag(hpi, 12)) - 1) %>%
  na.omit()

hpi_pct %>% 
ggplot(aes(x = pct_change_12_mons, y = pct_change, color = division)) +
  geom_point() + #alpha = .5
  facet_wrap(~division, ncol = 4) +
  labs(x = "% change (1 mo.)", y = "% change (1 yr.)") +
  theme(legend.position = "none",
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        plot.title = element_text(hjust = 0.5))
```


## Scatterplot with trend line

We can also add multiple geoms to a `ggplot` object, e.g. adding a trend line to our scatterplots:

```{r}
hpi_pct %>% 
ggplot(aes(x = pct_change_12_mons, y = pct_change, color = division)) +
  geom_point() + #alpha = .5
  geom_smooth(method = "lm",  se = TRUE, color = "purple") +
  facet_wrap(~division, ncol = 4) +
  labs(x = "% change (1 mo.)", y = "% change (1 yr.)") +
  theme(legend.position = "none",
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        plot.title = element_text(hjust = 0.5))
```



## Histogram

There are lots of ways to customize the look and feel of your plots:

```{r}
hpi_pct %>% 
  ggplot(aes(x = pct_change)) +
  geom_histogram(fill = "darkblue", color = "darkred", bins = 50) +
  facet_wrap(~division) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  theme_minimal()
```


## Density

```{r}
hpi_pct %>% 
  ggplot(aes(x = pct_change)) +
  geom_density(fill = "darkblue", color = "darkred", bins = 50) +
  facet_wrap(~division) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5)) +
  theme_minimal()
```


## Histogram and Density

```{r}
hpi_pct %>% 
  ggplot(aes(x = pct_change)) +
  geom_histogram(fill = "darkblue", color = "darkred", bins = 20) +
  geom_density(color = "red") +
  facet_wrap(~division) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
```


## Shading for recession

We can even combine datasets on the same plot. Let's create a geom to shade the background of a plot during recession periods.

```{r}
# First, create our recessions tibble with tribble()
recessions <- 
tribble(
  ~Peak, ~Trough,
  "1948-11-01", "1949-10-01",
  "1953-07-01", "1954-05-01",
  "1957-08-01", "1958-04-01",
  "1960-04-01", "1961-02-01",
  "1969-12-01", "1970-11-01",
  "1973-11-01", "1975-03-01",
  "1980-01-01", "1980-07-01",
  "1981-07-01", "1982-11-01",
  "1990-07-01", "1991-03-01",
  "2001-03-01", "2001-11-01",
  "2007-12-01", "2009-06-01",
  "2020-02-01", "2020-05-01"
  ) %>% 
  mutate(Peak = ymd(Peak),
         Trough = ymd(Trough))


recession_shade <- 
  geom_rect(data = recessions, 
            inherit.aes = F, 
            aes(xmin = Peak, 
                xmax = Trough, 
                ymin = -Inf, 
                ymax = +Inf), 
            fill = 'pink', 
            alpha = 0.5)


hpi_pct %>% 
  ggplot(aes(x = ymd(date), y = pct_change, color = division)) +
  recession_shade +
  geom_line() +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1),
        plot.title = element_text(hjust = 0.5),
        plot.subtitle = element_text(hjust = 0.5),
        plot.caption = element_text(hjust=0)) +
  ylab("") +
  xlab("Percent change, monthly") +
  ggtitle("Housing Price Appreciation", 
          subtitle = "by US Census Division") +
  labs(caption = "data source: FHFA") +
  scale_x_date(limits = c(as.Date(min(hpi_pct$date)), as.Date(max(hpi_pct$date)))) 
```


# `timetk` for time series data

The [`timetk`](https://business-science.github.io/timetk/index.html) package includes a bunch of functions that make working with time series data super easy. This includes functions for easily creating great looking plots of time series data:

```{r}
hpi_pct %>% 
  ungroup() %>% 
  plot_time_series(date, pct_change, .color_var = division, .smooth = FALSE)
```


## Anomaly diagnostics with `timetk`

`timetk` also includes functions for automatic anomaly detection:

```{r}
hpi_pct %>% 
  filter(division == "south_atlantic_sa") %>% 
  ungroup() %>% 
  plot_anomaly_diagnostics(date, pct_change)
```


# Plotly and `ggplotly()`

`timetk`'s interactive plots rely on [plotly](https://plotly.com/r/), a library for building interactive JavaScript visualizations. Plotly is supported in several different languages (including R) and has its own syntax.

Importantly, the `plotly` R package includes a function called `ggplotly()` that (you guessed it!) turns ggplots into plotly charts.

```{r}
hpi_plot <- ggplot(hpi_tidy, aes(x = date, y = hpi, color = division)) +
  geom_line()

hpi_plot %>% 
  ggplotly()
```






